All telecommunication systems have the objectives of transmitting signals with minimal signal loss, and with the highest possible signal to noise ratio (SNR). Also, in order to simplify the transmitting system's architecture and reduce its power requirements, it is desirable that signal transmissions be successfully accomplished with limited bandwidth requirements. To further these purposes, filters are often used in transmission systems to reduce bandwidth requirements and to minimize unwanted noise (interference) during a signal transmission.
In the context of the present invention, it is to be understood that many data signals are digitally generated as a stream of bits. Accordingly, digital signal processing techniques are typically considered. It is known, however, that digital processing techniques are generally impractical at high data rates.
With a view toward processing digital data signals at high data rates, it is to be appreciated that these signals can be characterized as a sequence of symbols which are akin to a frequency. In this characterization, each symbol includes an integer number of bits, and each symbol in the sequence has a same duration time, T. A transmitting device can then put symbols onto a channel at a symbol rate, Rs, with T=1/Rs. An important consequence of this is that by using techniques well known in the pertinent art, digital signals can be effectively processed as analog signals.
As implied above, many telecommunications systems incorporate low pass filters for the purpose of limiting a system's bandwidth requirements. As the name implies, low pass filters are designed to pass signals having frequencies which are below a predetermined stop bandwidth frequency. Because the signals are sinusoidal in nature, it happens that the signal level will begin to noticeably diminish at the higher frequencies in a bandwidth which are near, but below, the stop bandwidth frequency.
It is, of course, desirable to effectively use all frequencies in a bandwidth. To do this, a particular type of filter which comes closest to maximizing the useful bandwidth response is a low pass filter which is commonly referred to as a “Nyquist filter.” Ideally, a Nyquist filter will reduce the required bandwidth for transmitting a data signal, and it will do so without degrading the signal.
With the above in mind, it is an object of the present invention to present methodologies which employ empirical, analog signal processing techniques for designing and assembling tapped delay filters that provide a Nyquist filter response in a telecommunications system. In another aspect, it is an object of the present invention to provide methodologies using analog techniques for equalizing a simple low pass filter to manufacture an analog Nyquist filter having sophisticated performance characteristics. Another object of the present invention is to provide methodologies for use in the manufacture of analog Nyquist filters that rely solely on altering the hardware characteristics of filter components. It is also an object of the present invention to design a Nyquist filter that is capable of processing digital signals at high data rates. Still another object of the present invention is to provide methods for designing and assembling analog Nyquist filters which are easy to implement, are simple to modify in order to accommodate specific implementations, and are cost effective.